Surface critical behavior of semi-infinite systems with cubic anisotropy at the ordinary transition

TL;DR

This paper investigates the surface critical behavior of semi-infinite anisotropic cubic models at the ordinary transition using field theory and two-loop calculations, revealing new surface critical exponents for certain anisotropy regimes.

Contribution

It provides the first two-loop estimates of surface critical exponents in cubic anisotropic models, identifying a new universality class for n>n_c.

Findings

Surface critical exponents differ for n>n_c.

For n<n_c, the system belongs to the isotropic universality class.

New surface critical behavior characterized by distinct exponents.

Abstract

The critical behavior at the ordinary transition in semi-infinite n-component anisotropic cubic models is investigated by applying the field theoretic approach in d=3 dimensions up to the two-loop approximation. Numerical estimates of the resulting two-loop series expansions for the critical exponents of the ordinary transition are computed by means of Pade resummation techniques. For $n<n_{c}$ the system belongs to the universality class of the isotropic n-component model, while for $n>n_{c}$ the cubic fixed point becomes stable, where $n_{c}<3$ is the marginal spin dimensionality of the cubic model. The obtained results indicate that the surface critical behavior of the semi-infinite systems with cubic anisotropy is characterized by a new set of surface critical exponents for $n>n_{c}$.